Numerical solutions of singular time-fractional PDEs
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Omar Abu Arqub
Abstract
In this chapter, we propose and analyze a computational algorithm for the numerical solutions of singular time-fractional partial differential equations of Dirichlet function types. By interrupting the n-term of exact solutions, numerical solutions of linear and non-linear singular time-fractional equations of non-homogeneous function type are studied from a mathematical viewpoint. The accuracy properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the presented algorithm and simulated annealing provide a good scheduling methodology to such singular fractional equations.
Abstract
In this chapter, we propose and analyze a computational algorithm for the numerical solutions of singular time-fractional partial differential equations of Dirichlet function types. By interrupting the n-term of exact solutions, numerical solutions of linear and non-linear singular time-fractional equations of non-homogeneous function type are studied from a mathematical viewpoint. The accuracy properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the presented algorithm and simulated annealing provide a good scheduling methodology to such singular fractional equations.
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Fractional differential equations with bio-medical applications 1
- Fractional-order modeling of electro-impedance spectroscopy information 21
- Numerical solutions of singular time-fractional PDEs 43
- A multi-scale model of nociception pathways and pain mechanisms 55
- Variable-order derivatives and bone remodeling in the presence of metastases 69
- Skeletal muscle modeling by fractional multi-models: analysis of length effect 95
- Fractional calculus for modeling unconfined groundwater 119
- Fractional calculus models in dynamic problems of viscoelasticity 139
- Fractional calculus in structural mechanics 159
- Anomalous solute transport in complex media 193
- Application of variable-order fractional calculus in solid mechanics 207
- Fractional heat conduction models and their applications 225
- Index 247
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Fractional differential equations with bio-medical applications 1
- Fractional-order modeling of electro-impedance spectroscopy information 21
- Numerical solutions of singular time-fractional PDEs 43
- A multi-scale model of nociception pathways and pain mechanisms 55
- Variable-order derivatives and bone remodeling in the presence of metastases 69
- Skeletal muscle modeling by fractional multi-models: analysis of length effect 95
- Fractional calculus for modeling unconfined groundwater 119
- Fractional calculus models in dynamic problems of viscoelasticity 139
- Fractional calculus in structural mechanics 159
- Anomalous solute transport in complex media 193
- Application of variable-order fractional calculus in solid mechanics 207
- Fractional heat conduction models and their applications 225
- Index 247
